The invention describes a method for determining the temperature of a surface and more particularly, to a method for determining the temperature of a surface during a coating process by emissivity-correcting pyrometry.
Temperature measurement and control is important in coating processes that can occur in fields of manufacture such as coated optics, high-capacity optical components, integrated optical circuits and semiconductor and electronic components. In particular, temperature measurement and control is a critical factor in the growth of thin films by either chemical vapor deposition (CVD) or molecular beam epitaxy (MBE). It is particularly important in metal-organic CVD (MOCVD) thin film growth because compound semiconductors must often be grown with a very specific stoichiometry in order to maintain stringent lattice-matching conditions. The chemical reactions responsible for this CVD growth are often highly temperature dependent. Control of the deposition temperature thus becomes critical. Unfortunately, such control is difficult to achieve. The CVD environment employs reactive and toxic chemicals at high temperatures and requires the utmost in cleanliness to avoid unintentional doping or parasitic chemical reactions. Physical probes of the surface temperature cannot be used in such an environment.
Classical optical pyrometry, which measures the thermal emission from the hot surface is a strong candidate for a remote, in situ temperature probe. However, as thin films, such as those grown in semiconductor processes on wafer, are deposited, the emissivity of the surface can change dramatically. The emissivity change has two consequences. First, the heat loss from the surface, such as a wafer, due to thermal emission is changed by the presence of the thin film. This alters the balance in heat transfer and causes the surface temperature to change as the thin film growth is taking place. Second, a pyrometer that does not account for the emissivity changes will yield grossly inaccurate values for the surface temperature. It is not uncommon to encounter errors as large as 50xc2x0 C. To avoid these errors, emissivity changes must be measured and appropriate corrections made to extract an accurate surface temperature.
One method to correct, at least to some extent, pyrometry measurements of temperature is reflectance-correcting pyrometry. The method is a specialized application of emissivity-correcting pyrometry. Thermal radiation from an idealized blackbody surface is described by the well-known Planck formula:                     L        b            ⁢              (                  λ          ,          T                )              ⁢          ⅆ      λ        =                    c                  1          ⁢          L                                      λ          5                ⁢                  (                                    ⅇ                                                c                  2                                /                                  λ                  ⁢                  T                                                      -            1                    )                      ⁢          ⅆ      λ      
where C1L and c2 are the first and second radiation constants, respectively. Lb is the spectral radiance of the blackbody. For typical temperatures encountered in thin film growth (approximately 400xc2x0 C. to 1200xc2x0 C.), it is convenient to measure thermal radiation at a wavelength of 900 nm (generally with xc2x130 nm). Under these conditions, the Planck formula is virtually identical in value to the simpler Wien approximation:                     L        b            ⁢              (                  λ          ,          T                )              ⁢          ⅆ      λ        ≅                    c                  1          ⁢          L                            λ        5              ⁢          ⅇ                        -                      c            2                          /                  λ          ⁢          T                      ⁢          ⅆ      λ      
A quantity proportional to thermal radiance can be measured by detecting the radiation from a spot of area A, gathering light over a solid angle of emission, xcexa9, and a narrow range of wavelengths, xcex94xcex. This thermal radiation signal, s, is described by:
s=fLbAxcexa9xcex94xcex=Cexe2x88x92c2/xcexT
where f and C are instrumental proportionality factors. An experimental value of s may be used to invert the above equation to extract the temperature from a blackbody, provided that the instrument is calibrated at least at one known temperature to effectively determine C. This is the fundamental basis for single-wavelength blackbody pyrometry.
The blackbody is, however, an idealization. No real surface actually emits thermal emission according to the above equations. The radiance of any real surface is described in terms of the emissivity, xcex5:
L(xcex,xcex8,xcfx86,"sgr",T)=Lb(xcex,T)xcex5(xcex,xcex8,xcfx86,"sgr",T)
Emissivity is defined to be the fraction of thermal radiation emitted by a surface at wavelength xcex, exit angle xcex8, azimuthal angle xcfx86, polarization "sgr", and temperature, T, compared to a blackbody at the same temperature, T, and wavelength, xcex1. It can be, and generally is, a strong function of all its parameters, and is thus difficult to measure in practice. However, under conditions typically used in the manufacture of thin films, the emissivity is determined by measuring the specular reflectance. This is possible by using Kirchhoff""s law, which gives an unconditional relationship between the emissivity of a surface and another materials property, the absorptivity, xcex1.
xcex1(xcex,xcex8,xcfx86,"sgr",T)=xcex5(xcex,xcex8,xcfx86,"sgr",T)
The absorptivity is defined to be the fraction of electromagnetic energy absorbed by a material at temperature, T, when exposed to a beam of radiation with wavelength xcex, incidence angle xcex8, azimuthal angle xcfx86, and polarization a. For a blackbody, xcex1=1, independent of xcex, xcex8, xcfx86, "sgr", or T. For a real material, xcex1 less than 1, and a can be a strong function of all the parameters above. To take advantage of Kirchhoff""s law, the values of the wavelength, angle, and polarization must all be the same for the emissivity and absorptivity functions. This is important in the construction of an instrument that actually measures absorptivity as an indirect measurement of emissivity.
The final connection to specular reflectance is made using three assumptions specifically applicable to thin film semiconductor growth. The first assumption is that the semiconductor wafer is opaque. If a pyrometry wavelength is chosen too far below the bandgap of a substrate, this assumption may not be valid. However, it is generally possible to choose an above-bandgap wavelength for all but a few semiconductors. The second assumption is that the wafer remains smooth and flat during deposition. Under these conditions, an incident beam of light will scatter only in the specular direction and the reflected light beam is easily measured. If the surface becomes rough during deposition, then the formulas that follow are not valid. The third assumption is that the specular reflectance does not depend on azimuthal angle, xcfx86. This is generally true for compound semiconductors for which the reflectance anisotropy is typically less than one part in a thousand. This assumption is not strictly necessary to relate absorptivity to specular reflectance, but is convenient for practical applications on rotating wafers. If the above three assumptions apply, the following relationship between absorptivity and specular reflectance, R, is true:
xcex1(xcex,xcex8,xcfx86,"sgr",T)=1xe2x88x92R(xcex,xcex8,"sgr",T)
The following relationship can thus be derived:       L    ⁢          (              λ        ,        θ        ,        σ        ,        T            )        =            [              1        -                  R          ⁢                      (                          λ              ,              θ              ,              σ              ,              T                        )                              ]        ⁢                  c                  1          ⁢          L                            λ        5              ⁢          ⅇ                        -                      c            2                          /                  λ          ⁢          T                    
This relationship is the emissivity-correcting pyrometry expression for a smooth, flat, opaque surface during thin film growth. It relates a thermal emission radiance, L, and a specular reflectance, R, to the surface temperature, T. This expression can be considered well-known (see e.g., Bobel, et. al. J. Vac Sci Technol. B 12 (1994) 1207). However, determination of the specular reflectance function R(xcex,xcex8,"sgr",T) requires some method to take into consideration the variations that occur because of film growth and in the presence of stray background thermal emission.